Reliability Growth Analysis.

This function performs reliability growth analysis using the Crow-AMSAA model by Crow (1975) https://apps.dtic.mil/sti/citations/ADA020296 or piecewise NHPP model by Guo et al. (2010) doi:10.1109/RAMS.2010.5448029. It fits a log-log linear regression of cumulative failures versus cumulative time. The function accepts either two numeric vectors (times, failures) or a data frame containing both. The Piecewise NHPP model can automatically detect change points or use user-specified breakpoints.

Usage

rga(
  times,
  failures,
  model_type = "Crow-AMSAA",
  breaks = NULL,
  conf_level = 0.95
)

Arguments

times: Either a numeric vector of cumulative failure times or a data frame containing both failure times and failure counts. If a data frame is provided, it must contain two columns: times and failures. The times column contains cumulative failure times, and the failures column contains the number of failures at each corresponding time.
failures: A numeric vector of the number of failures at each corresponding time in times. Must be the same length as times if both are vectors. All values must be positive and finite. Ignored if times is a data frame.
model_type: The model type. Either Crow-AMSAA (default) or Piecewise NHPP with change point detection.
breaks: An optional vector of breakpoints for the Piecewise NHPP model.
conf_level: The desired confidence level, which defaults to 95%. The confidence level is the probability that the confidence interval contains the true mean response.

Value

The function returns an object of class rga that contains:

times: The input cumulative failure times.
failures: The input number of failures.
n_obs: The number of observations (failures).
cum_failures: Cumulative failures.
model: The fitted model object (lm (linear model) or segmented).
residuals: Model residuals on the log-log scale. These represent deviations of the observed log cumulative failures from the fitted values and are useful for diagnostic checking.
logLik: The log-likelihood of the fitted model. The log-likelihood is a measure of model fit, with higher values indicating a better fit.
AIC: Akaike Information Criterion (AIC). AIC is a measure used for model selection, with lower values indicating a better fit.
BIC: Bayesian Information Criterion(BIC). BIC is another criterion for model selection
breakpoints: Breakpoints (log scale) if applicable.
fitted_values: Fitted cumulative failures on the original scale.
lower_bounds: Lower confidence bounds (original scale).
upper_bounds: Upper confidence bounds (original scale).
betas: Estimated beta(s). Betas are the slopes of the log-log plot.
betas_se: Standard error(s) of the estimated beta(s).
growth_rate: Estimated growth rate(s). Growth rates are calculated as 1 - beta.
lambdas: Estimated lambda(s). Lambdas are the intercepts of the log-log plot.

Details

The scaling relationship between the size of input data (numbers of observations) and speed of algorithm execution is approximately linear (O(n)). The function is efficient and can handle large data sets (e.g., thousands of observations) quickly. The function uses the segmented package for piecewise regression, which employs an iterative algorithm to estimate breakpoints. The number of iterations required for convergence may vary depending on the data and initial values. In practice, the function typically converges within a few iterations for most data sets. However, in some cases, especially with complex data or poor initial values, it may take more iterations.

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
result1 <- rga(times, failures)
print(result1)
#> Reliability Growth Analysis (RGA)
#> ---------------------------------
#> Model Type: Crow-AMSAA 
#> 
#> 
#> Number of observations (failures): 5
#> Parameters (per segment):
#>   Growth Rate: 0.2013
#>   Beta: 0.7987 (SE = 0.0562)
#>   Lambda: 0.0269
#> 
#> Goodness of Fit:
#>   Log-likelihood: 4.78
#>   AIC: -3.55
#>   BIC: -4.72

df <- data.frame(times = times, failures = failures)
result2 <- rga(df)
print(result2)
#> Reliability Growth Analysis (RGA)
#> ---------------------------------
#> Model Type: Crow-AMSAA 
#> 
#> 
#> Number of observations (failures): 5
#> Parameters (per segment):
#>   Growth Rate: 0.2013
#>   Beta: 0.7987 (SE = 0.0562)
#>   Lambda: 0.0269
#> 
#> Goodness of Fit:
#>   Log-likelihood: 4.78
#>   AIC: -3.55
#>   BIC: -4.72

result3 <- rga(times, failures, model_type = "Piecewise NHPP")
#> Warning: Breakpoint estimate(s) outdistanced to allow finite estimates and st.errs
print(result3)
#> Reliability Growth Analysis (RGA)
#> ---------------------------------
#> Model Type: Piecewise NHPP 
#> 
#> Breakpoints (original scale):
#> 300.03 
#> 
#> 
#> Number of observations (failures): 5
#> Parameters (per segment):
#>   Growth Rates: 0.0598, 0.2881
#>   Betas: 0.9402, 0.7119
#>   Std. Errors (Betas): 0.2131, 0.255
#>   Lambdas: 0.0132, 0.0484
#> 
#> Goodness of Fit:
#>   Log-likelihood: 5.92
#>   AIC: -1.84
#>   BIC: -3.80

result4 <- rga(times, failures, model_type = "Piecewise NHPP", breaks = c(450))
#> Warning: Breakpoint estimate(s) outdistanced to allow finite estimates and st.errs
print(result4)
#> Reliability Growth Analysis (RGA)
#> ---------------------------------
#> Model Type: Piecewise NHPP 
#> 
#> Breakpoints (original scale):
#> 450 
#> 
#> 
#> Number of observations (failures): 5
#> Parameters (per segment):
#>   Growth Rates: 0.0598, 0.2881
#>   Betas: 0.9402, 0.7119
#>   Std. Errors (Betas): 0.2131, 0.255
#>   Lambdas: 0.0132, 0.0484
#> 
#> Goodness of Fit:
#>   Log-likelihood: 5.92
#>   AIC: -1.84
#>   BIC: -3.80

Usage

Arguments

Value

Details

See also

Examples